Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

Ecological management important for the persistence and biodiversity of ecosystems is considered in two general contexts. First, optimal management of invasive species is considered by adapting a linear-quadratic control model which is a dynamic optimization method that accounts for spatially explicit dynamics. Second, methods for ecosystem-based management of Caribbean coral reefs are developed by accounting for various aspects of an analytic model describing the dynamics of coral-algal interactions. The model in its simplest form exhibits hysteresis between two alternative stable states, one with high levels of coral cover and the other a degraded coral-depleted state with corresponding high levels of macroalgae. Extensions are made to explicitly consider exploitation of herbivorous reef fish which are important in supressing macroalgal overgrowth of coral. Importantly, this formulation provides a concrete example of ecosystem-based management by determining how fisheries management fits into the wider ecosystem impact. Other aspects of this system are considered, including the role of time delays in grazer response to changes in habitat as well as the long term effects of multiple interacting coral stressors, namely fishing effort and hurricane impacts.